The Purge of June 3rd is not as critical for the Avalanche as the demanding events in the rest of the month.

The Avs must sign the right coach, from the American Hockey League; sign the right goal protector, from the Swedish Elite League; and secure the right player, from the three potential stars available in the NHL draft.

The once-proud, twice-champion Avalanche was in crumple, collapse, out-of-crease mode from September to May.

The hockey club cannot swoon in June.

The Avalanche on Wednesday deep-sixed six — coach Tony Granato, three of his assistants, an assistant general manager and even the unfortunate video coordinator.

Greg “Who?” Sherman, who had been another bean-calculating assistant general manager, survived the sweeping, and sweeping out, and surprisingly was named the GM. The company man has to make his own sweeping moves straight away.

Although Pierre Lacroix remains the man in front of the throne — and made the announcement of the firings in a written statement — he, truthfully, is debilitated from complications of knee surgery, and isn’t able to oversee the daily operations of the organization.

Lacroix’s medical setback and recovery process have left the Avs in a holding pattern for seven weeks since the end of the dreadful, last-place, 45-loss, no-playoffs season. He did dump general manager Francois Giguere immediately and offered the head coaching position to Patrick Roy — who ultimately turned it down — but Lacroix can’t be on scene, and was persuaded by other team officials (and owner Stan Kroenke) this week that the Avalanche had to take a swift turn before the draft and the free-agency period.

Lacroix’s role will be limited during the summer, although he certainly will be consulted by Sherman on major decisions.

Starting with a coach.

There will be the usual suspects — former NHL coaches — but the Avs should hire a fresh prospect, following in the tradition of Marc Crawford and Bob Hartley, who each coached the Avs to Stanley Cups. The Avalanche already is considering the promotion of their AHL Lake Erie coach, Joe Sacco, but he has produced two mediocre, not monster, seasons with the Monsters.

The next coach should be Manitoba’s Scott Arniel, whose Moose (Meese?) are tied 1-1 with the Hershey Bears in the Calder Cup. Arniel was chosen AHL coach of the year. (Crawford was hired by Lacroix after receiving the same award, and both are from Ontario.)

Listen to the recent public praise from analyst extraordinaire Don Cherry. “He’ll be in the National Hockey League, guaranteed. He’s a players’ coach; you can see that. He knows what’s going on because he played so long.”

The 46-year-old Arniel spent a dozen journeyman years with three NHL teams, served his assistant coaching apprenticeship with Buffalo and has a 141-73-26 record, and playoff appearances all three seasons (with and has a chance at the title) in Manitoba. He’s ready.

Arniel doesn’t have a name, NHL reputation and potential fan draw as Roy does, but St. Patrick didn’t want the job. The names, the reputations and the potential fan draws must not emanate from the coach or the GM, anyway.

The Avs need to win again to win back Colorado, as the Nuggets did.

As important as appointing the right head coach (Arniel), Sherman must get the right goalie — Sweden’s Jonas Gustavsson, who has narrowed his preferences to four teams, including the Avs. (Countryman Peter Forsberg has encouraged him to emigrate to Denver.) Craig Billington, who has been promoted to vice president of etc., traveled to Sweden to meet with Gustavsson and his agent. Recruitment of the goalie, a European free agent, must be pushed harder.

And, with the No. 3 overall pick in the draft, the Avalanche has to make the right pick. It has been claimed that they can’t make a bad pick, given that the top three candidates supposedly will be NHL star- caliber players.

In all likelihood center John Tavares will go first, but the second player is not so set. The Avalanche will end up with either center Matt Duchene or defenseman Victor Hedman. The 6-foot-6 smooth and swift Hedman would be a special snare.

The Swedish quinella of Gustavsson, 24, and Hedman, 18, would be a payoff of 2009 Kentucky Derby proportions. Sweden has been very, very good to the Avalanche and the Red Wings.

Oh, and before Sherman sits down in the bigger office, he also must make a call to Joe Sakic and beg him to affirm he’s returning.

General Sherman has his marching orders. From purge to surge. Get a lot done soon, in June.

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